a) Field of the Invention
The present invention relates to a lens system which consists of a combination of one or two radial type graded refractive index lens element having a refractive index distribution in the direction perpendicular to the optical axis and one or two diffraction type lens element.
b) Description of the Prior Art
The radial type graded refractive index lens element which has a refractive index distribution in the direction perpendicular to the optical axis has very high capabilities to correct aberrations as described, for example, in the Applied Optics, Vol 21., pages 993-998. This literature clarifies that the radial type graded refractive index lens element makes it possible to compose, only of two lens elements, the conventional standard lens system for cameras which comprises six lens elements.
The radial type graded refractive index lens element has a refractive index distribution expressed by the following formula: EQU n(y)=N.sub.0 +N.sub.1 y.sup.2 +N.sub.2 y.sup.4 +. . .
wherein the reference symbol y represents the distance as measured from the optical axis to a lens portion of interest in the direction perpendicular to the optical axis, the reference symbol n(y) designates the refractive index of the lens element as measured at the portion located at the radial distance y, the reference symbol N.sub.0 denotes the refractive index of the lens element as measured at the portion located on the optical axis, and the reference symbols N.sub.1, N.sub.2, . . . represent the refractive index distribution coefficients.
The refractive index distribution coefficients of the radial type graded refractive index lens element have values which are different dependently on wavelengths. When the symbols such as d, F, C, etc. which represent wavelengths are suffixed to the refractive index distribution coefficients, for example in the forms of N.sub.id, N.sub.iF and N.sub.iC (the refractive index distribution coefficients for the d-line, F-line and C-line respectively), the Abbe's number representing dispersion is expressed as follows: EQU v.sub.i =N.sub.id /(N.sub.iF -N.sub.iC)
(i=1, 2, . . . )
Out of the Abbe's numbers mentioned above, v.sub.1 represents an approximate amount of chromatic aberration to be produced by a ray which is refracted by a medium.
Further, the basic Abbe's number (Abbe's number as measured on the optical axis) v.sub.0 is expressed by the following formula: EQU v.sub.0 =(N.sub.0d -1)/(N.sub.0F -N.sub.0C)
One of the high aberration correcting capabilities of the radial type graded refractive index lens element is the capability to correct chromatic aberration. Paraxial color PAC which is to be produced by the radial graded refractive index lens element is given by the following formula (i): EQU PAC=(-y.sub.a.sup.2 /n'.sub.ak) (.phi..sub.H /v.sub.0+.phi.G /V.sub.1) (i)
wherein the reference symbol y.sub.a represents height of ray, the reference symbol n'.sub.ak designates the angle of the ray emerging from the lens element relative to the optical axis, the reference symbol .phi..sub.H denotes the refractive power of the surface of the graded refractive index lens element and the reference symbol .phi..sub.G represents the refractive power of the medium of the graded refractive index lens element.
In order to allow the radial type graded refractive index lens element to fully exhibit the capability thereof for correcting chromatic aberration, it is necessary that (.phi..sub.H /v.sub.0+.phi.G /v.sub.1) has a small value in the formula (i). For this purpose, v.sub.1 must have a large value or a negative value. When v.sub.1 has a small value, remarkable paraxial color will be produced as is understood from the formula (i).
However, it is known that the radial type graded refractive index lens element can actually be manufactured easily only with materials having small values of v.sub.1 within a range on the order from 10 to 30. This is understood from the fact that the materials for the radial type graded refractive index lens elements which have hitherto been prepared in practice by the ion-exchange method, etc. have values of v.sub.1 within the range mentioned above. This fact is also stated in literatures, for example, the Applied Optics, Vol 25, pages 3351-3355.
Consequently, radial type graded refractive index lens elements which can actually be manufactured easily in practice have a defect that they produce remarkable chromatic aberration.